To meet today's demand for high-speed cost-effective communications, optical transmission systems having increased data capacity are highly desirable. One approach used in modern high-capacity transmission systems to increase the aggregate data-rate of transmission systems is to use a technique called dense wavelength division multiplexing (DWDM). In DWDM, an optical transmission link is divided into a plurality of channels with each channel having its own center frequency. Data transmitted on a particular channel is then affected by modulating the optical carrier at the center frequency of that channel. At the receiver, a band-pass filter tuned to the center frequency of the channel is used for detecting and demodulating the transmitted signal. By combining a plurality of channels in this manner, the aggregate data capacity of the optical link is increased. A limitation in increasing the aggregate data-handling capacity of DWDM optical transmission systems, however, is the amount of separation required between adjacent channels sufficient to reduce cross-channel interference to acceptable levels. Channel separations in the range of 50 GHz-100 GHz are commonly used to achieve sufficient separation.
However, the aggregate data rate presently achievable in conventional optical transmission systems is still orders of magnitude below the total capacity of optical fibers. In other words, the spectral efficiency (defined as the ratio between the aggregate bit rate transmitted over the optical link and the total optical bandwidth) of conventional transmission systems is not maximized for many reasons. First, the need to maintain channel separation of between 50-100 GHz to reduce interference between channels reduces the number of channels that can be multiplexed on the optical link. As a result, the aggregate bit rate of the optical link is limited thereby reducing the spectral efficiency of the transmission system. Also, because dispersion and nonlinearities in the optical transmission link limits the modulation bandwidth, and thus the bit-rate of any particular signal channel, the spectral efficiency of the system is decreased. As such, robust and cost efficient modulation formats for increasing spectral efficiency are of high interest for optical transmission systems.
For example, spectrally efficient signaling techniques, such as duobinary signaling, have been investigated in an attempt to reduce the spectral bandwidth required for each particular channel so that more channels can be supported by an optical link. In duobinary signaling, the required spectral bandwidth for a channel is reduced by manipulating the phase of the output data symbols transmitted over that channel. In duobinary, the data to be output consists of a combination of zeros and ones. In various duobinary signaling arrangements, the phase of the output data symbols are selected as follows: 1's in the input data stream that are separated by an even number of 0's have an identical phase in the duobinary signal output while 1's that are separated by an odd number of 0's have an opposite phase to that of the previously output 1. For example, the input data sequence {1, 1, 0, 1, 0, 0, 1, 1} is converted to a duobinary signal output of {1, 1, 0, −1, 0, 0, −1, −1} where −1 denotes a data bit having an opposite phase of a 1 data bit. Although duobinary signaling does increase the spectrally efficiency of the transmission system by narrowing the spectral bandwidth required for a channel, an improvement in bandwidth efficiency with duobinary signaling is limited to a factor of the square root of two (2) and there is no improvement in the tolerance of a signal to nonlinear effects caused by transmission of the signal along an optical path.